Do we have anything like accuracy and loss in RNN models?
RNN's stand for Recurrent Neural Networks which is, in fact, Deep Learning.

There has to be a loss since you're dealing with supervised learning and the typical loss metrics used are the same as you would see in feedforward networks (usually binary cross-entropy), the main difference being loss would be calculated between the true label at a particular time stamp $(t)$ and the prediction made from the subset of the network until time-stamp $(t-1)$. This leads the loss to act on all timestamps. 

Accuracy metrics also would be used in the same way such as Mean Square Error or L1. For more details you can go through this link. 

Hope this was helpful!